Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ H(3,ℤ/4) |
| Sylow | C5 ⋊ #4531 |
| Sylow | C3 ⋊ #64751 |
188 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|a^2=c,b^2=d,e^2=f,b^a=be,d^a=df,g^a=g^2,h^a=h^4,c^b=cf162 conjugacy classes — view the full character table.
| maximal subgroup of | D15×H(3,ℤ/4), C2×#11746352, D5×#4531, … |
| maximal normal subgroup of | D15×H(3,ℤ/4), C2×#11746352, D5×#4531, … |
| maximal quotient of | #14276698, #14276701, #14276714, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 547);